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By T. L. Loucks, E. T. Guerrero

Pressure drop characteristics in a system composed of two adjacent concentric regions of different permeability were studied. The differential equations for continuity of mass flow in the two regions were solved using the Laplace transformation and the necessary boundary conditions to give the pressure distribution in the composite reservoir, the resulting equation for pressure drop at the inner boundary was evaluated for a variety of composite reservoirs and compared with the results for a uniform reservoir. From this study it was found that under certain conditions the permeability in both zones, as well as the size of the inner zone, can be determined from the pressure drop curve. INTRODUCTION The theory for the pressure distribution and pressure build-up behavior of a well producing a single, slightly compressible fluid from infinite and finite homogeneous reservoirs was presented by Hornerl and Miller, Dyes and Hutchinson.2 Extensions on this original work to provide improved and extended interpretations and better agreement between theory and observed results have been made by Matthews, et a1,3 van Everdingen,4 Gladfelter, et al5 Stegemeierand Matthews,6 Hurst and Guerrero,7 and Perrine.8 More recently Lefkovits, et al,9 studied pressure build-up behavior in bounded reservoirs composed of stratified layers. Houpeurtl0 has suggested various approaches to the general problem of variable permeability and porosity but presented no analytic solutions for particular permeability variations. Albert, Jaisson and Marionll studied the finite composite reservoir and presented numerical solutions to the unsteady-state case and an analytical solution valid only for large times. They also studied the so-called pseudo-steady state for several examples of radial permeability variations. Very similar examples have been treated in the unsteady state with application to pressure build-up by Loucks in an unpublished manuscript. More recently Hurst12 has presented the complete point-sink solution (valid for all times) for the infinite composite reservoir. He applied these solutions to interference between oil fields along with an even more elegant application of his explicit solution to the material-balance equation including water influx. Mortada 13 approaches the same application by avoiding the point-source limitation but gives the solution for the aquifer region which is valid only for large times. Hopkinson, Natanson and Temple14 have treated both the finite and infinite composite reservoir obtaining the pressure distribution for the inner zone valid for large times. This paper presents a theoretical study of the pressure distribution in an infinite composite reservoir composed of two adjacent concentric regions of different permeability. The object was to determine the manner in which pressure drop at the inner boundary of a composite reservoir depends upon time, the permeability of each zone and the size of the inner zone. Expressions for the pressure distribution in both zones are developed which take into account the radius of the sink and are valid for small times as well as large times. It was felt that an understanding of the pressure drop behavior in various composite reservoirs would be of assistance in the interpretation of some pressure build-up curves which do not behave according to the theory derived for uniform systems. Often the region surrounding the wellbore is either more permeable or less permeable than the reservoir because of the various drilling and completion practices. The effects of reduced permeability due to drilling-fluid invasion and of increased permeability due to fracturing or acidizing need to be more carefully defined. Therefore, an equation for the pressure drop in a composite reservoir was developed, and the effects of both the permeability in each zone and the size of the inner zone were studied. STATEMENT AND SOLUTION OF PROBLEM BOUNDARY CONDITIONS AND ASSUMPTIONS The physical system studied was a composite

Many definitions have been advanced and many limitations advocated in the use of the terms, veins, lodes and ledges. The following definitions appear to follow the best usage. [ ] A fissure vein, according to Lindgren, is a mineral mass tabular in form as a whole, though often irregular in detail, filling or accompanying a fracture or series of closely set and intimately related parallel fractures in the enclosing rock, the mineral mass having been formed later than both the country rock and the

Jan 1, 1932

By William Braden

In view of the current discussion of a proposed change in the United States mining law, abolishing the feature known as the extralateral right of a lode-location, it is an interesting circumstance that in the neighboring Province of British Columbia this feature was tried for eight years and then abandoned. The results of that abandonment have been such as to disprove the proposition, so confidently advanced by many

Jan 1, 1899

AT the meeting of the Board of Directors held on June 25, 1926, and in response to numerous in-dividual suggestions for changes, a committee on Re-vision of the Constitution and By-Laws of the Insti-tute was appointed, consisting of C. F. Rand, Archi-bald Douglas and H. Foster Bain. Various confer-ences were held, much correspondence conducted and a preliminary draft was prepared. It proved imprac-ticable to complete the work in time to submit the matter to the membership for approval or disapproval at the annual meeting in 1927, and the Committee was continued with instructions to prepare a report as a basis of action in 1928. After Mr. Rand's death George Otis Smith was appointed in his place and the tentative draft herewith submitted has been pre-pared in its present form by Messrs. Smith, Douglas and Bain, though not differing in any material mat-ter from an earlier draft approved by Mr. Rand. In preparing this the Committee has kept in mind primarily the desirability of simplification and of making the By-Laws conform to the actual practice of the Institute as worked out through experience. The Constitution and By-Laws adopted in 1912, and which with minor amendments only still govern the Insti-tute, are full of specific provisions regarding pro-cedure; such as that laid down for guidance of the Papers and Publications Committee. Many of these have proved unworkable and in practice have not been always strictly followed. It now seems wise to write into the Constitution and By-Laws only the general fun-damental principles to he followed and to provide for such easy change in methods of following them out as will permit efficient conduct of the business. It is this thought that has guided the Committee in rewrit-ing many of the sections. With this in view also the Constitution, as such, has been shortened to the brief-est feasible statement of fundamentals. All matters relating to means of making these principles effec-tive have been put into the By-Laws or in the hands of committees whose work is subject to control and whose rules are subject to approval or disapproval by the Board of Directors. Many suggestions for changes have come to the Committee that have not been incorporated in this draft. Some of these are in themselves excellent but have not been incorporated here because the Commit-tee discovered no sentiment for them such as would be likely to secure their approval, or found them out of harmony with the general plan followed herein.

Jan 9, 1927

By E. A. H. Tays, F. A. Schiertz

In 1893 the Anglo-Mexican Mining Company, Limited, purchased the Guadalupe and adjoining mines, and, after opening up the Guadalupe, constructed a 20-stamp mill, which was started in August, 1894. Although the results were extremely profitable (the ore being very rich and carrying much free gold) they were not satisfactory, because the tailings were found to average about $20 per ton in gold. Early in 1895 the late Mr. James E. Mills made for the company a very thorough study of the subject, and decided that the tailings could be treated most advantageously by the cyanide process. In view of this opinion, Mr. Henry R. Batcheller, of Boston, was sent down in the winter of 1895-96 to experiment on a working scale. Mr. Batcheller was successful; and, during 1896-97, built a cyanide-plant with a capacity for treating 1500 tons per month. This was run until May, 1899, when all the sands suitable for the process had been treated. The mill was stopped about the same time for lack of ore; but no tailings from the mill had gone to the dump since October, 1897, as the values they contained after that date were far too low to warrant further treatment. When the cyanide-plant was stopped there still remained on the dump about 16,000 tons of slimes, consisting of about 75 per cent. of clay-slimes and 25 of sand-slimes. The successful treatment of this very unfavorable material is the theme of this paper. Fig. 1 is a view of the hacienda, taken in 1897.

Jan 1, 1902

By Arthur Crowfoot

Page IntRodUction ................... The Round Table in Lake Superior Practice .........420 Early Use of Revolving Round Table in Butte District...... Use oF the Round Table at GREat Falls foR Sand-Slime Feed ., . The Round Table for Fine Slime........,.... Construction of Slime Plant at Great Falls..... '..... 424 Tests on Wood, Linoleum, and Cement Decks.........426 Central Feed Apron Removed ....'......... Re-treatment of Round-Table Tailing........... Determination of Conditions for Round-Table Treatment of Slimcs ... 430 Variation in Slope of Round-Table Deck........ ,... The Steel-Frame Cement-Deck Round Table ........ Tests on Cement and Canvas Dock Surfaces ..: ..... Conoidal Deck Round Tables............. Results with Sand-Slime Feed on Conoidal Deck....... Conclusions from Preliminary Tests on Conoidal and Conical Decks ... 446 Discussion of Results of Four-Day Test on Conical and Conoidal Decks . 452 Discussion of Results of Eight-Day Test.......... Qualitative Sampling of Concentrates Across Conical Deck.... Summary of Slime-Plant Practice............ Suggested Flow Sheet for Slime Classification and Treatment.... Conclusion...................467 Introduction The principal object of this paper is 60 presest, data on the development of the revolving convex round table as a concentrator for the through 0.07-mm. slimes from the ores of the Butte district, although some brief notes on the earliest recorded use of this type of concentrating table in the ore-dressing plants of the Lake Superior region and of the Butte district are also presented. The revolving convex round table belongs to the class of concentrating tables known as film-sizing. tables, these tables using the relative transporting power of a film, or thin sheet of water, as it flows over a quiet inclined surface, to separate the minerals of a sorted product. The grains of heavy mineral move down the slope of the table deck slowly, or, in some cases, not at all, after the initial force of the feed entry VOL. XLIX.—27

Jan 1, 1915

By A. D. K. Laird, C. A. Johnson

Drag coefficients for a cylinder being towed through water at constant velocity and also at constant linear acceleration were measured. Drag coefficients for constant velocity towing showed reasonable agreement with previous results. The drag coefficients found for constant acceleration showed little correlation with either the magnitude of the acceleration or the value of the modulus AD/V2 and tended to be slightly lower than those for constant velocity. INTRODUCTION For the design of offshore structures, wave forces acting on immersed cylinders are of importance. Several investigations have been made of these forces and of how they can be predicted from wave theories. A paper by Crooke' summarizes much of the work already done. More recent research by the Wave Research Laboratory at the University of California, Berkeley, has added much to the body of data collected under ocean wave conditions, but has not found a reliable method of force prediction from basic theories of wave motion. The present investigation is part of a long-range program to collect data with which to test current and future theories and correlations. The immediate objective was to measure drag forces on a circular cylinder subjected to linear accelerations over the range of Reynolds numbers between l04 and 105 where the drag coefficient was a constant for constant velocities. In particular, the effect of constant acceleration from rest and from uniform motion was to be investigated. The effect of acceleration may be evaluated in terms of drag coefficients. A useful resistance coefficient, C, is defined by the equation for total drag force, D, exerted by the fluid on the cylinder. DT =CSp V2/2.........(1) The coefficient C may be plotted as a function of the parameter AD/V2. Here D is the diameter and S is the projected area of the cylinder. The acceleration and velocity are A and V. The mass density of the fluid is p. An alternate drag coefficient, C, corresponds to the total force of the fluid opposing the motion minus the virtual mass force. This drag coefficient, arising from the velocity of the fluid, may be compared with that for the same cylinder in uniform motion. The similarities and differences between this coefficient as calculated for accelerated and for steady motion are of interest in the inverse process of predicting drag forces on cylinders under arbitrary conditions. One serious difficulty in this method is the specification of the virtual mass which depends also on the flow picture about the cylinder.1 EXPERIMENTAL EQUIPMENT The experiment was performed in the combination wave and towing tank at the Engineering Field Station of the University of California. The tank is 200 ft long, 8 ft wide, and 6 ft deep. The tow carriage is externally propelled by a cable, and the velocity of the carriage is maintained essentially constant by means of an am-plidyne. For the purpose of the present investigation, the speed control of the amplidyne was modified by inserting a linear speed control rheostat, which was rotated at a constant speed by a small d-c motor equipped with a slip-clutch. Accelerations which were constant over a reasonable length of time were thus produced. The magnitude of the acceleration depended upon the speed of the d-c motor and the limiting speed of the carriage. Data were obtained for a range of accelerations of 2 to 10 ft/sec,2 and a range of velocities of 2 to 15 ft/sec. An accelerometer (Statham Type C-2-350) with a range of ±2g was attached to the carriage and connected to a Brush analyzer and penmotor. A continuous coil of wire with 10 turns/ft wound around a fixed wooden form extending for a distance of 40 ft along the length of the tank was connected by an electrical contact mounted on the carriage to a Brush analyzer and penmotor, to give the time-position history for each run. The test cylinder was machined from solid aluminum alloy, 17-ST. to a diameter of 1.250 in., and could be

Jan 1, 1957

Jan 1, 1969

By R. M. Caves

High-purity dense tungsten coating is obtained by means of a modified de Boer-van Arkel iodide process using tungsten bromides. The all-glass reaction system is pumped, baked, and sealed (pinched-off) at about 10-7 mm Hg pressure. The bromides then formed in situ are decomposed, depositing tungsten on heated tungsten surfaces. Heating of the specimen is done inductively in a novel arrangement that avoids electrodes of glass-to-metal seals. The tungsten, deposited at specimen temperatures from 2000° to 2800°F and bulb (halide) temperatures of 225" to 725°F, was adherent and uniform, and ranged in thickness to 1/8-in. REFRACTORY metals are of interest at NASA for use in hypersonic aircraft, in rocket engines, and in other thrust devices where very high temperatures are encountered. Tungsten, with a melting point about 6100° F, is potentially very useful for some of these applications. Considerable research on tungsten and its alloys is currently being conducted at the NASA Lewis Research Center. In this tungsten research program, there is need for a method of depositing high-purity, nonporous tungsten coatirlgs. Metallurgical bonding of the coating both to itself and to the substrate is required. In addition, it is necessary to be able to deposit thin, uniform coatings on substrates of a variety of shapes and sizes for laboratory test purposes. A survey of the methods previously used for depositing tungsten coatings indicated that none would likely meet these requirements for high purity, good uniformity, and high density except thermal decomposition of the halides. The method for coating that was selected for investigation was the thermal decomposition of tungsten bromide. This is a variation of the van Arkel and de Boer iodide process established years ago and recently reviewed.1,2 This process is applicable to the transition metals in general. More recently, the application and techniques were extended with chlorine3 and fluorine,4 and included the coating of tungsten. This is believed to be the first report on the use of the bromide for tungsten coating. Bromine was chosen over the other halogens because it promised a lower temperature for tungsten

Jan 1, 1962

By Blamey Stevens

(Butte Meeting, August, 1913.) THE following paper aims to make a full explanation of the phenomena of rock jointing: It may be unnecessary to give any general description of what are termed joints in rocks, but Professor Geikie's clear and faithful generalizations are so illuminating that no excuse need be given. for introducing the following and other quotations into this paper "Almost all rocks are traversed by vertical or highly inclined divisional planes termed joints. These have been regarded as due in some way to contraction during consolidation (fissures of retreat) ; and this is no doubt their origin in innumerable cases. But, on the other hand, their frequent regularity and persistence across materials of very varying texture suggest rather the effects of internal pressure and movement within the crust." 1 General Explanation.-In this paper I show that the phenomenon of jointing may to a large extent be accounted for by the pressure of the water contained in the pores of the rock. To understand this, each constituent grain of the porous material may be considered to be separately compressed by the water which submerges it. As all the grains are held together by cohesion, the whole mass is contracted by this pressure. In an indefinitely extended mass, however, there must be a limit to the possible contraction without rupture, because the material is restrained from moving freely by other material around its boundaries. The mass of rock thus becomes broken up. This phenomenon is known as '" shrinkage " jointing. The term " shrinkage " is an apt one, if it be understood that the shrinkage of the rock is often brought about by change of stress. Stresses.-The compressive component of water stress on the individual grains is evidently the same as that of the water with which it is in contact. This is so, both before and after the jointing is formed. Before the jointing is formed there is, however, a tensile stress in one or more directions which keeps the material from contracting. .

Jan 7, 1913

By Don Coulter

OBSERVATIONS were made over a period of seventeen months to ascertain the economic value of a four-cycle Miller engine direct-connected to a Watts compressor, to determine whether this type of engine could compete suc-cessfully against the old type of two-cycle engine in general use. The accompanying tables show the data obtained. The first, over a period of seventeen months, compares the operating cost per hour and cost per horsepower-hour with

Jan 8, 1928

By Howard V. Sears

ArcHodrilling (Arcuate Hole Drilling) of short radius overhead curved holes from within the working level with a new, small-diameter in-the-hole drill produces tangible, assayable chip samples from the entire height of the projected mine level where the hole arcs down immediately in front of the working face. Drilling through the projected level with diamond coring tools produces samples showing the competence of roof and floor strata as well as the geological and economic characteristics of the ore. Hand-portable solid state electronic surveying instrument has been developed to survey the ArcHole and a convenient nomograph plotting record sheet converts survey digital readouts to hole inclination in degrees, to radius of curvature in feet, and to attitude of the plane of curvature from vertical in degrees, all without calculation. The ArcHodrilling system offers a tool with which the exploration geologist can more nearly assess the true potential of old mining properties being reexamined and to reduce the number of surface diamond drill holes needed to secure development data about new ore bodies. It gives the mine geologist an opportunity to secure those data at a fraction of the cost of drilling from the surface. The mining supervisor has a convenient, cheap tool to look ahead to know what he will be mining tomorrow. The mill supervisor has an opportunity to reduce his mineral loss in tailings by being able to anticipate the grade of his mill feed.

Jan 1, 1973

By E. A. Holbrook

Research, primarily, is finding out the truth. Research applied to enigeering opens the door to new principies and processes, the application of which benefits mankind in a material way. The engineer believes that investigation instituted with the primary view of making the results directly applicable to the industries is the highest type of research. Coal is essentially the basis of modern industrial civilization; therefore, any considerable research pertaining to coal must link itself to the industry by practical application of the results of the research. In other words, all investigational work connected in any way with coal leads to conclusions that permit a better understanding of the origin, nature of occurrence, composition, better and safer mining, more careful preparation, or greater efficiency in utilization of coal. Modern engineering research has been fostered essentially by universities and in the laboratories of institutions of learning. Coal problems that lend themselves to solution in the laboratories have been first attacked and are perhaps the farthest toward solution. For example, a great amount of research work has been carried out with the various phases of chemistry connected with coal. On the other hand, the equally important problems connected with methods of mining have received but little attention, primarily because their solution involves the continued use of a great and expensive laboratory, which is none other than the mine itself. As many of the problems already solved have had chemistry as their background, so many of the problems unsolved have physics as their background; there are also unsolved problems that deal in coal economics. Even psychology must be called upon in future coal-mining research as a basis for solving those great problems that deal with human relationships. 'In general, considerable advance has been made in coal research dealing with chemistry, not so much progress has been made with problems having physics and engineering as a background, while there is a tremendous range of untouched problems that deal essentially with business and psychology. Research in coal mining is not a new development. In the chronicles of the northern coal trade as published in the Transactions of the North

Jan 1, 1920

By R. S. Handy

DOES hand-sorting of mill feed pay? The fact that the practice is so general would seem to indicate that there must be good reasons for following it; yet, to my mind, the advantage in many cases is doubtful enough to invite a thorough discussion of the subject, in an effort to determine under what conditions hand-sorting does pay. A typical sorting plant in the Coeur d'Alene district handles about 800 tons of mine-run ore per day. The material is run over a grizzly with about 4-in. opening; the oversize is crushed to about 4-in. size and joins the undersize, and the whole product is washed and screened on trommels with about 1 ½ -in. openings. The oversize from these trommels is spread on a belt and the waste and first-class ore are sorted out by hand, the residue being further crushed, and passes, together with the trommel undersize, into the mill feed bins. About 50 tons of shipping ore and 150 tons of waste are sorted out per day, leaving about 600 tons of mill feed. To sort out this material requires 20 ore sorters and five bosses and repairmen. The normal cost of hand-sorting is about 16 c. per ton of run-of-mine ore, or 65 c. per ton of material sorted out. I believe that straight crushing and milling of the run-of-mine ore, in this case, is not only cheaper, but is metallurgically moree canonical and efficient than hand-sorting followed by milling of the residue. At one of the Bunker Hill rock-houses, 1250 tons of run-of-mine ore are reduced to pass 30-mm., or about 1 ¼ -in. opening in six hours, requiring five men. The equipment and the power consumed are not greatly different from that required in a sorting plant of the same capacity, and the normal cost of thus preparing the feed for milling is under 3 c. per ton of mine product. The relative cheapness of this method as against hand-sorting is thus clearly established, the saving being about 13 c. per ton. If there is any virtue in hand-sorting, then, it must lie in the metallurgical results achieved.

Jan 4, 1918

By Hsun Hu, R. S. Cline

A detailed studj) of texture formation in 2 pet Al-Fe single crystals with initial orientations of approximately (111) [112], (112) [111], and (112) [111] was made by examining the textures developed on the surface and at various interior sections of the crystal after rolling to various amounts. Depending' upon the initial orientation of the crystal, the surface and interior textures may differ only in sharpness, or may differ essentially in orientation. The orientation of the (111) [112] crystal does not change upon rolling up to 70 pet, but after rolling more than 90 pet a distinct component of (001) (110] orientation is developed. The texture formed in the two (112) (1111 type crystals consists of (111) (1121 and (001) (1101 components. The latter, however, is largely confined to the surface layers. The textures formed on both sides of the crystal are identical, and the texture composition profile is approximately symmetrical with respect to the central section of the strip thickness. The formation of these texture components is analyzed. DURING the past seven or eight years, deformation and recrystallization textures in rolled Si-Fe single crystals have been extensively studied by various investigators.1-7 From these studies, much knowledge on texture formation in bee crystals of various initial orientations was obtained. However, these results also raised many questions, regarding particularly the correlation between deformation and recrystallization textures, as well as the deformation texture itself of some particular crystals. To take a (111) [112] type crystal as an example, it was shown by Dunn and Koh2, 3 that this orientation does not change during deformation by rolling. This finding is consistent with the conclusion reached by Barrett and Leven-son8 with respect to iron crystals that (111) [112] is one of the stable end orientations. However, different recrystallization textures were observed by Dunn and Koh3 in (111) [112] type crystals of different initial thickness, which widened differently during rolling even though their deformation textures were identical. Another interesting example, also from the results of Dunn and Koh2'3 is that of texture formation in a (112) [111] crystal. This crystal developed a two-component deformation texture of (111) [112] plus (001) [110]. Its recrystallization texture, however, was found to be predominantly (110) [001], which is related to the (111) [112] component by a simple [110] rotation. This crystal, therefore, behaved as if the other deformation texture component, (001) [110], were not present. There are also discrepancies among the results of different investigators, as well as numerous unexplained fine features of the deformation texture of crystals of various initial orientations. In order to have a better understanding of all of these points, a detailed study of deformation textures is greatly needed. One of the obvious things that has been completely overlooked in previous texture studies is the possible effect of surface texture. All past work on the texture of Si-Fe single crystals was conducted in a rather simple manner, i.e., the rolled crystals were etched to a very thin sheet; then their textures were examined by transmission X-ray techniques. For recrystallization texture studies, unless precautions are taken by etching off a sufficient amount of the surface layer before annealing, the texture developed in the interior may be affected by the surface layer, which may well have a different initial texture and which may have undergone recrystallization earlier than the interior of the specimen. Because of this effect, it is now planned to reexamine the texture of various rolled and annealed single crystals at the surface, and at various sections below the surface by using reflection techniques. In some cases, both surfaces of the rolled crystal will be examined. In one of Dunn's early papers,9 he noted that at an early stage of rolling the crystal seems to divide roughly through the middle to become a sample which in effect consists of two layers having some what different orientations. This effect has never been further explored. The investigation described in the present paper constitutes the beginning of a series of thorough investigations of texture formation in deformed bee single crystals designed to clear up some of the uncertainties which have been discussed. We have chosen a high-purity 2 pet Al-Fe alloy for this investigation. It is known that the allotropic transformation of iron is eliminated by alloying with approximately 1petAl. Such an alloy, being very similar to silicon ferrite, can be heated to the solidus temperature without phase transformation. One reason for choosing A1-Fe instead of Si-Fe for the present investigation is that we have been able to make single crystals of a vacuum-melted high-purity A1-Fe alloy by the strain-anneal method without much difficulty, but were not successful in doing so with a vacuum-melted high-purity Si-Fe alloy. For many research purposes,

Jan 1, 1962

By Glenn C. Waterman

THE diamond drill is a very important tool in exploration and development testing and its use is increasing. In almost all cases results of diamond drilling are analyzed on the basis of grade and tons. A proper evaluation of core and sludge assays is important if drilling results are to be acceptable as a basis for geologic and engineering appraisal. The relatively wide variation in assay averages as calculated by various well-known combining methods indicates that the engineering choice of a method may affect the outcome of the drilling in terms of ore and waste. The problem of combining assay results from core and sludge samples has been discussed many times in conference and in the literature.'" Most writers agree that the field of disagreement in methods is large and that the engineer on the job must consider features unique to his drilling, pick one of several combining methods, and depart from the rules when abnormal results come in. All the discussion to date can be summed up by the admission that as yet there is no fairly simple, generally acceptable combining method that is practicable over a wide range of drilling conditions, ground conditions, and ore occurrence.

Jan 1, 1955

By A. M. Gaudin

IN flotation lime is used to depress pyrite. For this purpose it is preferred to caustic soda. The low cost of lime and the widespread availability largely account for this preference. However, there is some evidence1 that pyrite is more readily depressed by calcium than by sodium ions at the same pH. To measure the difference in adsorption of calcium and sodium, which is thought to lie at the basis of the differences in depressing action, radionuclides of

Jan 2, 1953

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed. Flotation involves the selective levitation of mineral and its transfer from cell to launder. The flotation rate is the rate of this transfer. It may be defined by the slope of a recovery-time curve for any cell in a bank, or at any time in batch operation. The objective in flotation rate study is an equation expressing the rate in terms of some measurable property of the pulp. This can be either the concentration of floatable mineral in weight per unit volume1,2 or a relative concentration, which will be a function of the recovery." A rate equation for an actual flotation pulp will contain at least two constants, both to be determined from the data. One of these, the initial concentration or proportion of floatable mineral, is not necessarily equal to the feed assay because of nonfloatable oversize or locked particles." The other, a rate constant, is a measure of proportionality between the rate and the pulp property on which the rate depends. The value of the rate constant will be determined by the values of all variables which control the process and will be changed by significant changes in any of them. It is, therefore, a direct measure of performance. Where recovery or grade change continuously with flotation time, the rate constant will be independent of time and will characterize the entire course of the separation. Development of Rate Equations Rate equations can be developed either by analysis of the mechanism of the process or by direct fitting of equations to recovery-time data. Sutherland&apos;s attempt by the first method&apos; suggests that the effect of particle size variation on the rate complicates the derivation of a simple equation applicable to an ore pulp. A further problem with an ore is the concentrate grade requirement, which usually involves a variable rate of froth removal. Thus the final rate for any cell may depend on the froth character and froth height, as well as on the pulp composition. This does not imply that each cell cannot reach a steady state2 in which the rate will depend ultimately on pulp composition. The second method is the fitting of rate equations consistent with the necessary boundary conditions* to experimental recovery-time curves. On the assumption that under constant operating conditions the flotation rate is proportional to the actual or relative concentration of floatable mineral in the pulp, a generalized rate equation may be expressed as follows: Rate = Kcn [I] where K is the rate constant, c is some measure of the quantity of floatable mineral in the pulp at time t, and n is a positive number. In previous rate studies, the value of n has been taken as 1, either by direct assumption," or as a result of the hypothesis that bubble-particle collision is rate determining.&apos; A first order equation results, which after integration in terms of cumulative recovery R, leads to Loge A/A-R = Kt [2] The quantity A is the maximum possible recovery with prolonged time under the conditions used. No conclusive proof for the validity of this equation in flotation has been advanced. The evidence cited in its support consists entirely in the demonstration that it appears to apply to a limited number of recovery-time curves."&apos; It will be shown subsequently that this procedure is not sufficient to establish the order of a flotation rate equation. The possibility that the equation may be of higher order therefore requires examination. If, in particular, the exponent in eq 1 is assumed to be 2, then after integration there results R = A2Kt/1 + AKt [3] with K again a rate constant and A the maximum proportion of recoverable mineral. Eq 3 may be

Jan 1, 1952

By R. C. Schmidt, B. E. Kennedy

The Mont Klahoyo magnetite deposit is located about 600 km (373 miles) northwest of Abidjan, Ivory Coast. During an exploration period ending in 1977 an international joint venture group investigated the deposit and proved reserves of 670 Mt (739 million short tons) grading 36% iron. The deposit occurs at the northeast end of the Baoubly-Kiriao chain of Precambrian iron formations with associated amphibolites, pyroxenites, and gneisses of the Liberian Shield. The ore body is represented by a highly metamorphosed banded quartz-magnetite iron formation with alternating beds of iron silicates and quartz-magnetite. Amphibolite-pyroxenites and sillimanite-cordierite-garnet gneisses form hanging and footwall rocks. The iron formation has been folded into an elongated, overturned 2-shaped major drag fold with axes trending and plunging approximately northeast. Beds are vertical or dip steeply to the southeast. The ore zone has an average thickness of 130 m (427 ft) and outcrops intermittently over a distance of approximately 5.5 km (3.4 miles). Based upon detailed studies of drill cores and the results of ore dressing test work, eight stratigraphic units, identified as K- 1 to K-8, are recognizable in the iron formation. Four interbedded units are low grade silicate zones (silicate facies) while the remaining quartz-magnetite units are oxide facies, representing the important Mont Klahoyo deposit ores. Ore-bearing "K" units are subdivided further into 11 ore types, based upon their specific lithologies, iron content, and concentration characteristics. Identification of these ore types proved particularly useful to mine planning and flowsheet design. A cap of oxidized material overlies the primary quartz- magnetite iron formation, but no enrichment has occurred. It is thought that the Mont Klahoyo iron formations were deposited chemically in a volcanic environment as a siliceous iron formation with volcanism the primary source of iron and silica. Metamorphism converted the siliceous iron formation to a coarse-grained, quartz-magnetite-silicate iron formation.

Jan 1, 1983